Question: Rewrite as a simplified fraction. ${1.\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 13.3333...\\ 1x &= 1.3333...\end{align*}}$ Subtracting the two equations, we have: ${9x = 12}$ ${x = \dfrac{12}{9}} $ ${x = \dfrac{4}{3}} \text{or} {1 \dfrac{1}{3}}$